Problem: Add the following rational expressions. $\dfrac{8k^2+4}{5k^2+5}+\dfrac{k^3-k+8}{5k^2+5}=$
Explanation: We want to add two rational expressions whose denominators are equal. We can do this by adding the numerators and keeping the denominator the same. [Does this fit with how we add rational numbers?] $\begin{aligned} &\phantom{=}\dfrac{8k^2+4}{5k^2+5}+\dfrac{k^3-k+8}{5k^2+5} \\\\ &=\dfrac{(8k^2+4)+(k^3-k+8)}{5k^2+5} \\\\ &=\dfrac{8k^2+4+k^3-k+8}{5k^2+5} \\\\ &=\dfrac{k^3+8k^2-k+12}{5k^2+5} \end{aligned}$ In conclusion, $\dfrac{8k^2+4}{5k^2+5}+\dfrac{k^3-k+8}{5k^2+5}=\dfrac{k^3+8k^2-k+12}{5k^2+5}$